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2006-10-17
On the Image Approximation for Electromagnetic Wave Propagation and PEC Scattering in Cylindrical Harmonics
By
, Vol. 66, 65-88, 2006
Abstract
Aclosed-form formula, the discrepancy parameter, which has been defined as the ratio of the modal expansion coefficients between the electromagnetic field obtained from the image approximation and the incident electromagnetic field, has been proposed for the evaluation of the validity of the image approximation in the electromagnetic wave propagation, i.e., Love's equivalence principle, and the electromagnetic wave scattering, i.e., the induction equivalent and the physical equivalent, in the cylindrical geometry. The discrepancy parameter is derived through two equivalent methods, i.e., the vector potential method through the cylindrical addition theorem and the dyadic Green's function method, for both the TE and TM cylindrical harmonics. The discrepancy parameter justifies the fact that the image approximation approaches the exact solution for the cylindrical surface of infinite radius. For the narrow-band field with limited spectral component in k space, the cylindrical modal expansion of the electromagnetic wave into the TE and TM cylindrical harmonics can be separated into the forward-propagating wave that propagates forward and the back-scattered wave that is back-scattered by the PEC surface, within the image approximation. The discrepancy parameter shows that the validity of the image approximation depends on the property of the incident field and the radius of the cylindrical surface, i.e., the narrow-band field and the surface of a large radius are in favor of the image approximation, which has also been confirmed by the numerical result.
Citation
Shaolin Liao Ronald Vernon , "On the Image Approximation for Electromagnetic Wave Propagation and PEC Scattering in Cylindrical Harmonics," , Vol. 66, 65-88, 2006.
doi:10.2528/PIER06083002
http://www.jpier.org/PIER/pier.php?paper=06083002
References

1. Booysen, A. J., "Aperture theory and the equivalence principle," IEEE Antennas and Propagation Magazine, Vol. 45, No. 3, 29-40, 2003.
doi:10.1109/MAP.2003.1232161

2. Yaghjian, A. D., "Equivalence of surface current and aperture field integrations for reflector antennas," IEEE Trans. on Antennas and Propagat., Vol. 32, No. 12, 1355-1358, 1984.
doi:10.1109/TAP.1984.1143261

3. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, Inc., New York, 1989.

4. Lin, D.-B. and T.-H. Chu, "Bistatic frequency-swept microwave imaging: principle, methodology and experimental results," IEEE Transactions on Microwave Theory and Techniques, Vol. 41, No. 5, 855-861, 1993.
doi:10.1109/22.234522

5. Tseng, C.-H. and T.-H. Chu, "An effective usage of vector network analyzer for microwave imaging," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 9, 2884-2891, 2005.
doi:10.1109/TMTT.2005.854251

6. Schlobohm, B., F. Amdt, and J. Kless, "Direct PO optimized dualoffset reflector antennas for small earth stations and for millimeter wave atmospheric sensors," IEEE Transactions on Microwave Theory and Techniques, Vol. 40, No. 6, 1310-1317, 1992.
doi:10.1109/22.141365

7. Galindo-Israel, V., W. A. Imbriale, and R. Mittra, "On the theory of the synthesis of single and dual offset shaped reflector antennas," IEEE Trans. Antennas Propagat., Vol. AP-35, No. 8, 887-896, 1987.
doi:10.1109/TAP.1987.1144200

8. Hestilow, T. J., "Simple formulas for the calculation of the average physical optics RCS of a cylinder and a flat plate over a symmetric window around broadside," IEEE Antennas and Propagation Magazine, Vol. 42, No. 5, 48-52, 2000.
doi:10.1109/74.883507

9. Adachi, S., A. Ohashi, and T. Uno, "Iterative radar target imaging based on modified extended physical optics method," IEEE Trans. on Antennas and Propagat., Vol. 38, No. 6, 847-852, 1990.
doi:10.1109/8.55581

10. Legault, S. R., "Refining physical optics for near-field computations," Electronics Letters, Vol. 40, No. 1, 2004.
doi:10.1049/el:20040001

11. Borkar, S. R. and R. F. H. Yang, "Reflection of electromagnetic waves from oscillating surfaces," IEEE Trans. on Antennas and Propagat., No. 1, 122-127, 1975.
doi:10.1109/TAP.1975.1141013

12. Cramer, P. W. and W. A. Imbriale, "Speed up of near-field physical optics scattering calculations by use of the sampling theorem," IEEE Transactions on Magnetics, Vol. 30, No. 5, 3156-3159, 1994.
doi:10.1109/20.312607

13. Cao, R. and R. J. Vernon, Improved performance of threemirror beam-shaping systems and application to step-tunable converters, Joint 30th International Conference on Infrared and Millimeter Waves & 13th Internatioal Conference on Terahertz Electronics, 19-23, 2005.

14. Perkins, M. P. and R. J. Vernon, Iterative design of a cylinderbased beam-shaping mirror pair for use in a gyrotron internal quasi-optical mode converter, 29th International Conference on Infrared and Millimeter Waves, 27, 2004.

15. Liao, S. and R. J. Vernon, Anew fast algorithm for field propagation between arbitrary smooth surfaces, Joint 30th Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics, Vol. 2, 606-607, 2005.

16. Liao, S. and R. J. Vernon, "Sub-THz beam-shaping mirror designs for quasi-optical mode converter in high-power gyrotrons," J. Electromagn. Waves and Appl., Vol. scheduled for 21, No. 4, 425-439, 2007.

17. Harrington, R. F., Time-harmonic Electromagnetic Fields, McGraw-Hill, Inc., 1961.

18. Papa, R. J. and J. F. Lennon, "Conditions for the validity of physical optics in rough surface scattering," IEEE Trans. on Antennas and Propagat., Vol. 36, No. 5, 647-650, 1988.
doi:10.1109/8.192141

19. Tai, C.-T., The Dyadic Green's Function, IEEE Press, 1991.

20. Collin, R. E., Field Theory of Guided Waves, second edition, IEEE Press, 1991.

21. Stratton, J. A., Electromagnetic Theory, McGraw-Hall, Inc., 1941.

22. Leach, Jr. W. M. and D. T. Paris, "Probe-compensated nearfield measurements on a cylinder," IEEE Trans. on Antennas and Propagat., Vol. 21, No. 7, 435-445, 1973.
doi:10.1109/TAP.1973.1140520

23. Yaghjian, A. D., "An overview of near-field antenna measurements," IEEE Trans. on Antennas and Propagat., Vol. 34, No. 1, 30-45, 1986.
doi:10.1109/TAP.1986.1143727

24. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.

25. Li, L.-W., N.-H. Lim, W.-Y. Yin, and J.-A. Kong, "Eigenfunctional expansion of dyadic Green's functions in gyrotropic media using cylindrical vector wave functions," Progress In Electromagnetics Research, Vol. 43, 101-121, 2003.
doi:10.2528/PIER03020201